There exist different types of receivers for such systems having undergone linear precoding in sending mode.
Thus, J. J. Boutros and E. Viterbo (“Signal space diversity, a power and bandwidth-efficient diversity technique for the Rayleigh fading channel”, IEEE Trans. Commun., vol. 44, no. 4, pp. 1453-1467, July 1998) propose a signal space diversity technique, illustrated in FIG. 1, also called linear precoding 11, and demonstrates the fact that multidimensional rotation sending constellations augment this diversity without increasing the bandwidth of the signal. For Rayleigh type fading channels, this augmentation of diversity is expressed by an improvement of performance at reception. However, such a system necessitates the implementation of a maximum likelihood (ML) type receiver 12.
One drawback of these maximum likelihood type receivers is the complexity of their implementation. Indeed, the complexity of the algorithms increases exponentially as a function of the number of antennas and the number of states of the modulation.
A. Stamoulis, Z. Liu and G. B. Giannakis, in “Space-time block-coded OFDMA with linear precoding for multirate services” (IEEE Trans. Signal Processing, vol. 50, no. 1, pp. 119-129, January 2002), and V. Le Nir, M. Hélard and R. Le Gouable, in “Technique de précodage et de codage espace-temps” (Space-time precoding and encoding technique), patent application number FR 02 16200, filed on 16 Dec. 2002 on behalf of the present applicant) propose the association of the linear precoding with space-time block codes with a view to MIMO (“Multiple Input Multiple Output”) type transmission.
In particular, as illustrated in FIG. 2, V. Le Nir et al. propose the use of precoding matrices 21 which, combined with orthogonal space-time codes 22 before sending, allow linear decoding 23 in reception, simplifying the implementation of the receiver.
One drawback of these prior art techniques is that they are not optimal in the presence of channel coding, owing to a vestigial interference after “de-precoding”. Indeed, whatever may be the decoding algorithm used (whether of the maximum likelihood or linear type), this vestigial interference is not eliminated.
The term “de-precoding” here and throughout the rest of the document is understood to mean an operation that is substantially the reverse of the precoding operation performed at the time of sending.
Very recently, iterative techniques for the reception of a linearly pre-coded signal have appeared. The techniques improve performance at reception, when a channel coding is implemented in sending mode.
Thus, J. J. Boutros, N. Bresset and L. Brunel (“Turbo coding and decoding for multiple antenna channels”, International Symposium on Turbo Codes and Related topics, Brest, France, September 2003) have introduced a system, presented in FIG. 3, implementing linear precoding associated with space-time bit-interleaved coded modulation (ST-BICM) in a MIMO transmission. The system consists of the concatenation of a channel coder 31, an interleaver 32, a converter of binary elements into symbols 33 (also called a mapper), enabling the demultiplexing of the symbols on the different sending or transmit antennas and as well as the precoder 34 acting both in the time domain and the space domain.
At reception, the system implements a space-time demapper 35 using an ML type algorithm, analyzing especially the LLR (“log likelihood ratios”) on each coded bit. A demapper of this kind implements an operation that is substantially the reverse of that of the mapper. These likelihood ratios are improved through a SOVA (soft output Viterbi algorithm) type of channel decoder 36 and sent again to the demapper 35. This process is reiterated in order to improve the decoded data {circumflex over (d)}(p).
Z. Wang, S. Zhou and G. B. Giannakis in “Joint coding-precoding with low complexity turbo-decoding” (IEEE transactions on wireless communications, Vol. 3, No. 3, May 2004) have also presented an iterative receiver for a system that combines channel coding 41 and linear precoding 42 in sending or transmit mode as illustrated in FIG. 4. The receiver is based on an exchange of extrinsic information between a de-precoder associated with a maximum likelihood type of demapper 43 and a channel decoder 44.
These two iterative systems enable the joint performance of the de-precoding and the channel decoding within an iterative loop so as to approach optimum performance.
However, one drawback of these prior art iterative techniques is their complexity of implementation, owing to the use of a maximum likelihood type of algorithm at reception. Indeed, the complexity of such algorithms is exponentially proportional to the order of the modulation and the size of the precoding (or of the precoding matrices).
Other techniques for the reception of a signal having undergone a channel coding and a linear precoding before being sent are also known.
However, these techniques generally do not enable the interference due to the precoding, and as well as the interference due to channel coding or again to space-time coding to be eliminated, or at least reduced, with acceptable complexity.